[BUG] OpenTelemetry tool_name shows generic "mcp_tool" instead of full MCP tool name since v2.1.2

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

Since version 2.1.2, the OpenTelemetry tool_result event logs tool_name as the generic string mcp_tool instead of the full tool name format mcp__<server>__<tool>.
This breaks observability dashboards that track MCP server and tool usage patterns.

What Should Happen?

The tool_name attribute should contain the full MCP tool name, e.g.:

mcp__jira__search_issues
mcp__context7__get-library-docs
mcp__playwright__browser_click

Error Messages/Logs

Query aggregating tool_name by version shows the regression:
| Version | tool_name                          | count |
|---------|------------------------------------|-------|
| 2.1.1   | mcp__jira__search_issues           | 29    |
| 2.1.1   | mcp__figma__get_design_context     | 7     |
| 2.1.2   | mcp_tool                           | 144   |
| 2.1.3   | mcp_tool                           | 2254  |
| 2.1.29  | mcp_tool                           | 60    |

Last working version: 2.1.1
First broken version: 2.1.2

Steps to Reproduce

Enable OpenTelemetry logging:

export CLAUDE_CODE_ENABLE_TELEMETRY=1
export OTEL_LOGS_EXPORTER=otlp,console
export OTEL_EXPORTER_OTLP_ENDPOINT=http://localhost:4317

Use any MCP tool (e.g., call a Jira or Context7 tool)
Query the tool_result events and observe tool_name is mcp_tool instead of the full name

Claude Model

Not sure / Multiple models

Is this a regression?

Yes, this worked in a previous version

Last Working Version

2.1.1

Claude Code Version

2.1.29

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

_No response_